\((\frac{3}{{17}} + \frac{2}{5}) \times \frac{1}{4} = \)...

\(\begin{array}{l}(\frac{3}{{17}} + \frac{2}{5}) \times \frac{1}{4}\\ = (\frac{{15}}{{85}} + \frac{{34}}{{85}}) \times \frac{1}{4}\\ = \frac{{49}}{{85}} \times \frac{1}{4} = \frac{{49}}{{340}}\end{array}\)

\(\begin{array}{l}(\frac{5}{{19}} - \frac{1}{7}):\frac{2}{3}\\ = (\frac{{35}}{{133}} - \frac{{19}}{{133}}):\frac{2}{3}\\ = \frac{{16}}{{133}}:\frac{2}{3} = \frac{{24}}{{133}}\end{array}\)

\(\begin{array}{l}\frac{2}{{23}} \times \frac{3}{8} + \frac{1}{5}\\ = \frac{3}{{92}} + \frac{1}{5}\\ = \frac{{15}}{{460}} + \frac{{92}}{{460}} = \frac{{107}}{{460}}\end{array}\)

\(\begin{array}{l}\frac{4}{{25}}:\frac{2}{9} - \frac{1}{6}\\ = \frac{{18}}{{25}} - \frac{1}{6}\\ = \frac{{108}}{{150}} - \frac{{25}}{{150}} = \frac{{83}}{{150}}\end{array}\)

\(\begin{array}{l}(\frac{7}{{29}} + \frac{3}{{10}}) \times \frac{2}{7}\\ = (\frac{{70}}{{290}} + \frac{{87}}{{290}}) \times \frac{2}{7}\\ = \frac{{157}}{{290}} \times \frac{2}{7} = \frac{{314}}{{2030}} = \frac{{157}}{{1015}}\end{array}\)

\(\begin{array}{l}(\frac{5}{{21}} - \frac{2}{{13}}):\frac{3}{4}\\ = (\frac{{65}}{{273}} - \frac{{42}}{{273}}):\frac{3}{4}\\ = \frac{{23}}{{273}}:\frac{3}{4} = \frac{{92}}{{819}}\end{array}\)

\(\begin{array}{l}\frac{3}{{16}} \times \frac{4}{{15}} + \frac{2}{9}\\ = \frac{{12}}{{240}} + \frac{2}{9}\\ = \frac{1}{{20}} + \frac{2}{9} = \frac{9}{{180}} + \frac{{40}}{{180}} = \frac{{49}}{{180}}\end{array}\)

\(\begin{array}{l}\frac{2}{3} \times (\frac{1}{4} + \frac{3}{8})\\ = \frac{2}{3} \times (\frac{2}{8} + \frac{3}{8})\\ = \frac{2}{3} \times \frac{5}{8} = \frac{{10}}{{24}} = \frac{5}{{12}}\end{array}\)

\(\begin{array}{l}\frac{3}{6}:(\frac{2}{3} - \frac{1}{4})\\ = \frac{3}{6}:(\frac{8}{{12}} - \frac{3}{{12}})\\ = \frac{3}{6}:\frac{5}{{12}} = \frac{{36}}{{30}} = \frac{6}{5}\end{array}\)

\(\begin{array}{l}\frac{1}{8} \times (\frac{3}{4} - \frac{2}{6})\\ = \frac{1}{8} \times (\frac{9}{{12}} - \frac{4}{{12}})\\ = \frac{1}{8} \times \frac{5}{{12}} = \frac{5}{{96}}\end{array}\)

\(\begin{array}{l}\frac{4}{6}:(\frac{1}{3} + \frac{2}{8})\\ = \frac{4}{6}:(\frac{8}{{24}} + \frac{6}{{24}})\\ = \frac{4}{6}:\frac{{14}}{{24}} = \frac{4}{6}:\frac{7}{{12}} = \frac{{48}}{{42}} = \frac{8}{7}\end{array}\)

\(\begin{array}{l}\frac{3}{4} \times (\frac{2}{9} + \frac{1}{6})\\ = \frac{3}{4} \times (\frac{4}{{18}} + \frac{3}{{18}})\\ = \frac{3}{4} \times \frac{7}{{18}} = \frac{{21}}{{72}} = \frac{7}{{24}}\end{array}\)

\(\begin{array}{l}\frac{2}{8}:(\frac{3}{6} - \frac{1}{9})\\ = \frac{2}{8}:(\frac{9}{{18}} - \frac{2}{{18}})\\ = \frac{2}{8}:\frac{7}{{18}} = \frac{{36}}{{56}} = \frac{9}{{14}}\end{array}\)

\(\begin{array}{l}\frac{1}{3} \times (\frac{4}{8} + \frac{2}{4})\\ = \frac{1}{3} \times (\frac{4}{8} + \frac{4}{8})\\ = \frac{1}{3} \times \frac{8}{8} = \frac{1}{3} \times 1 = \frac{1}{3}\end{array}\)

\(\begin{array}{l}\frac{5}{6}:(\frac{2}{4} - \frac{1}{8})\\ = \frac{5}{6}:(\frac{4}{8} - \frac{1}{8})\\ = \frac{5}{6}:\frac{3}{8} = \frac{{40}}{{18}} = \frac{{20}}{9}\end{array}\)

\(\begin{array}{l}\frac{2}{5} \times \frac{3}{{10}}:\frac{1}{2}\\ = \frac{6}{{50}}:\frac{1}{2} = \frac{3}{{25}}:\frac{1}{2} = \frac{6}{{25}}\end{array}\)

\(\begin{array}{l}\frac{4}{{12}}:\frac{2}{7} \times \frac{3}{5}\\ = \frac{{28}}{{24}} \times \frac{3}{5} = \frac{7}{6} \times \frac{3}{5} = \frac{{21}}{{30}} = \frac{7}{{10}}\end{array}\)

\(\begin{array}{l}3 \times \frac{5}{2}:7\\ = \frac{{15}}{2}:7 = \frac{{15}}{{14}}\end{array}\)

\(\begin{array}{l}\frac{1}{2} + \frac{1}{3} \times \frac{2}{5}\\ = \frac{1}{{12}} + \frac{2}{{15}}\\ = \frac{{15}}{{30}} + \frac{4}{{30}} = \frac{{19}}{{30}}\end{array}\)

\(\begin{array}{l}\frac{3}{4} - \frac{1}{2}:\frac{2}{3}\\ = \frac{3}{4} - \frac{3}{4} = 0\end{array}\)

\(\begin{array}{l}\frac{2}{3} \times \frac{3}{5} + \frac{1}{4}\\ = \frac{6}{{15}} + \frac{1}{4}\\ = \frac{{24}}{{60}} + \frac{{15}}{{60}} = \frac{{39}}{{60}} = \frac{{13}}{{20}}\end{array}\)

\(\begin{array}{l}\frac{5}{6}:\frac{2}{3} - \frac{1}{3}\\ = \frac{5}{4} - \frac{1}{3} = \frac{{15}}{{12}} - \frac{4}{{12}} = \frac{{11}}{{12}}\end{array}\)

\[\begin{array}{l}\frac{1}{4} + \frac{2}{5}:\frac{3}{7}\\ = \frac{1}{4} + \frac{{14}}{{15}}\\ = \frac{{15}}{{60}} + \frac{{56}}{{60}} = \frac{{71}}{{60}}\end{array}\]

\(\begin{array}{l}\frac{3}{8} - \frac{1}{4} \times \frac{2}{3}\\ = \frac{3}{8} - \frac{2}{{12}}\\ = \frac{9}{{24}} - \frac{4}{{24}} = \frac{5}{{24}}\end{array}\)

\(\begin{array}{l}\frac{4}{5} \times \frac{2}{7} + \frac{1}{3}\\ = \frac{8}{{35}} + \frac{1}{3})\\ = \frac{{24}}{{105}} + \frac{{35}}{{105}} = \frac{{59}}{{105}}\end{array}\)

\(\begin{array}{l}\frac{2}{3}:\frac{1}{2} - \frac{3}{4}\\ = \frac{4}{3} - \frac{3}{4}\\ = \frac{{16}}{{12}} - \frac{9}{{12}} = \frac{7}{{12}}\end{array}\)

\(\begin{array}{l}\frac{1}{6} + \frac{3}{4} \times \frac{2}{5}\\ = \frac{1}{6} + \frac{6}{{20}}\\ = \frac{5}{{30}} + \frac{9}{{30}} = \frac{{14}}{{30}} = \frac{7}{{15}}\end{array}\)

\(\begin{array}{l}\frac{1}{3} \times \frac{4}{5} + \frac{2}{7}\\ = \frac{4}{{15}} + \frac{2}{7}\\ = \frac{{28}}{{105}} + \frac{{30}}{{105}} = \frac{{58}}{{105}}\end{array}\)

\(\begin{array}{l}\frac{3}{5}:\frac{1}{3} - \frac{1}{2}\\ = \frac{9}{5} - \frac{1}{2}\\ = \frac{{18}}{{10}} - \frac{5}{{10}} = \frac{{13}}{{10}}\end{array}\)

\(\begin{array}{l}\frac{2}{5} + \frac{1}{4} \times \frac{3}{8}\\ = \frac{2}{5} + \frac{3}{{32}}\\ = \frac{{64}}{{160}} + \frac{{15}}{{160}} = \frac{{79}}{{160}}\end{array}\)

\[\begin{array}{l}\frac{1}{2} \times \frac{3}{4} + \frac{1}{5}\\ = \frac{3}{8} + \frac{1}{5}\\ = \frac{{15}}{{40}} + \frac{8}{{40}} = \frac{{23}}{{40}}\end{array}\]

\(\begin{array}{l}\frac{5}{8}:\frac{1}{2} - \frac{2}{3}\\ = \frac{5}{4} - \frac{2}{3}\\ = \frac{{15}}{{12}} - \frac{8}{{12}} = \frac{7}{{12}}\end{array}\)

\(\begin{array}{l}\frac{3}{7} + \frac{2}{3} \times \frac{1}{4}\\ = \frac{3}{7} + \frac{2}{{12}}\\ = \frac{{36}}{{84}} + \frac{{14}}{{84}} = \frac{{50}}{{84}} = \frac{{25}}{{42}}\end{array}\)

\(\begin{array}{l}\frac{2}{3} \times \frac{1}{5} + \frac{3}{4}\\ = \frac{2}{{15}} + \frac{3}{4}\\ = \frac{8}{{60}} + \frac{{45}}{{60}} = \frac{{53}}{{60}}\end{array}\)

\(\begin{array}{l}\frac{5}{6}:\frac{3}{4} - \frac{1}{4}\\ = \frac{{20}}{{18}} - \frac{1}{2}\\ = \frac{{20}}{{18}} - \frac{9}{{18}} = \frac{{11}}{{18}}\end{array}\)

\(\begin{array}{l}\frac{1}{4} + \frac{2}{7} \times \frac{3}{5}\\ = \frac{1}{4} + \frac{6}{{35}}\\ = \frac{{35}}{{140}} + \frac{{24}}{{140}} = \frac{{59}}{{140}}\end{array}\)

\(\begin{array}{l}\frac{2}{5} \times \frac{4}{7} + \frac{1}{3}\\ = \frac{8}{{35}} + \frac{1}{3}\\ = \frac{{24}}{{105}} + \frac{{35}}{{105}} = \frac{{59}}{{105}}\end{array}\)

\(\begin{array}{l}\frac{4}{9}:\frac{2}{3} - \frac{1}{6}\\ = \frac{4}{6} - \frac{1}{6}\\ = \frac{3}{6} = \frac{1}{2}\end{array}\)

\(\begin{array}{l}\frac{1}{5} + \frac{3}{8} \times \frac{2}{7}\\ = \frac{1}{5} + \frac{6}{{56}}\\ = \frac{{56}}{{280}} + \frac{{30}}{{280}} = \frac{{86}}{{280}} = \frac{{43}}{{140}}\end{array}\)

\(\begin{array}{l}\frac{5}{7} - \frac{1}{4}:\frac{3}{5}\\ = \frac{5}{7} - \frac{5}{{12}}\\ = \frac{{60}}{{84}} - \frac{{35}}{{84}} = \frac{{25}}{{84}}\end{array}\)

\(\begin{array}{l}\frac{3}{5} \times \frac{2}{3} + \frac{1}{4}\\ = \frac{6}{{15}} + \frac{1}{4}\\ = \frac{{24}}{{60}} + \frac{{15}}{{60}} = \frac{{39}}{{60}} = \frac{{13}}{{20}}\end{array}\)

\(\begin{array}{l}\frac{2}{3}:\frac{1}{5} - \frac{3}{7}\\ = \frac{{10}}{3} - \frac{3}{7}\\ = \frac{{70}}{{21}} - \frac{9}{{21}} = \frac{{61}}{{21}}\end{array}\)